1. Field of the Invention
This invention relates to an adaptive process control system for controlling a process according to the dynamic characteristic of the process. More particularly, this invention relates to an adaptive process control system of the type in which, when the dynamic characteristic is unknown or changes with time and operating conditions, that characteristic is estimated or identified from a response waveforms (signals) of the process, and the controller parameters in the process controller are adjusted on the basis of the estimated dynamic characteristics, so as to optimize at all times the performances of the process control system for controlling the process variable.
2. Discussion of the Background
The adaptive process control system includes the PID auto-tuning controller, the self-tuning controller (STC), the model reference adaptive control system (MRACS), and the like. In the PID auto-tuning controller and the self-tuning controller, the parameters of the dynamic characteristic model of the process under control are estimated by using a least square type parameter estimation algorithm. The controller parameters are adjusted on the basis of the estimated results so that the closed loop control system optimizes a performance index. In the MRACS, the controller parameters of the adaptive process control are adjusted so that the process operates in exactly the same way as the reference model does.
In the PID auto-tuning controller and the self-tuning controller, the stability of the control system is not considered in adjusting (calculating) the controller parameters. Therefore, in some types of processes, the controlled variables of the process do not converge to the set-point, but contradistinctively diverse from it, resulting in the instability of the control system. In the MRACS, such a design is possible as to provide a stable process control system. To this end, many requirements are needed: the dead time, the highest order, and a difference between the pole and zero point (a difference of number of articles) must be known; the process must be minimum phase system. Actually, however, it is almost impossible to find the processes satisfying such requirements. Therefore, it is safe to say that this process control system is theoretically good, but bad in practice. Consequently, it is impossible to use the MRACS for a real plant to realize the stable process control system.
These types of adaptive process control systems are effective in controlling the process whose dynamic characteristic slowly varies, but ineffective in controlling the process whose dynamic characteristic rapidly varies. Specifically, in these control systems, the controller parameters can follow the slow variation of the dynamic characteristic so as to optimize the control system at all times. These control systems can not follow the quick variation of the dynamic characteristics, so that the control system is temporarily unstable in operation. Incidentally, examples of the rapid variation of the dynamic characteristic are rapid variations of the gain- and/or phase-frequency characteristics.
Additionally, when the low frequency drift disturbance is added to the control system or the measurement of the process variable signal suffers from noise, that disturbance or noise misleads the estimation of the dynamic characteristics of the control systems. The result is an erroneous adjustment of the controller parameters, possibly leading to an instable operation of the control system.
As described above, in the conventional adaptive process control system, the control system is sensitive to the nature of the process, the rapid change of the dynamic characteristic of the process, the drift disturbance, measuring noise, and the like.
In the process control system, for controlling temperature, flow rate (speed), pressure and the like of the plant, it is a common practice to construct the adaptive control system by appropriately combining various types of compensation modes, such as the proportional control (P) action, the integration control (I) action, and the derivative control (D) action. For example, in the PID control system, the controlling signal u(t) is obtained by the following PID formula EQU u(t)=C.sub.0 .intg.e(t)dt+C.sub.1 e(t)+C.sub.2.de(t)/dt (B-1)
where e(t) is a difference between a set-point r(t) and a process variable signal y(t), and C.sub.0 and C.sub.2 are the integration gain, the proportional gain, and the derivative gain as controller parameters, respectively.
In the I-PD control system, the controlling signal u(t) is obtained by the following I-PD formula EQU u(t)=K.intg.e(t)dt-f.sub.0 y(t)-f.sub.1.dy(t)/dt (B-2)
where K, f.sub.0, and f.sub.1 are the integration gain, the proportional gain, and the derivative gain as controller parameters, respectively.
In the adaptive control system, these controller parameters must be properly selected according to the dynamic characteritics of the process. One known method for selecting the controller parameters, which is available for both the PID control system and I-PD control system, is "The Design of a Control System on the Basis of the Partial Knowledge of a Process" by Toshiyuki Kitamori, Transactions of the Society of Instrument and Control Engineers, vol. 15, No. 4, pp. 549 to 555, August 1979. This approach is very useful in that the controller parameters of the control system can be obtained by using a simple formula from a denominator type transfer function of the process and the reference model representing the desirable characteristic of the control system.
In this approach, however, the gain margin and the phase margin are not considered in design. Therefore, the approach is unsatisfactory in designing control system for the process which has the step response of the overshoot or the reverse response. Further, the controller parameters as selected does not always ensure a stability of the control system.
When considering the PID control system alone, the design using the Bode diagram considering the gain margin and the phase margin has been well known. This method is based on the trial and error approach, and can not set the gain margin and the phase margin exactly satisfying the specifications of the control system. Therefore, it depends largely on the empirical knowledge. For example, in the process control system, the phase margin is 16.degree. to 80.degree.; and the gain margin is 3 to 9 dB. In a servo control system, the phase margin is 40.degree. to 65.degree. and the gain margin is 12 to 20 dB. Thus, these control systems employ relatively wide margins for these controller parameters. Therefore, the stability of the control system can be ensured, but it is unknown in the design stage whether or not the response waveform of the control system is the intended one. Therefore, preceding with the design, the designer constantly checks the response waveform whether or not it is the desired one, by gradually changing the gain margin and the phase margin. Thus, the designer must design the control system in the trial and error manner. For this reason, if this design method is used, it is impossible to automatically set the controller parameters.
As described above, the conventional controller parameter setting methods for the process control system can not exactly set the controller parameters which satisfy the desired characteristic of the control system for every type of compensating actions, such as PID, I-PD or 2 degree-of-freedom PID controller, and the lead/lag compensator. Therefore, a stability of the process control system cannot be anticipated before it is designed.
The known methods to measure the transfer function representing the dynamic characteristic of the process are the method using the servo analyzer, the correlation method, and the method in which parameters of an ARMA (autoregressive movement average) model are estimated using the method of least squares.
In the servo analyzer method, a sine wave signal as the identification signal is superposed on the controlling signal to the process. When the process is in a stationary state, an amplitude ratio of the input (controlling or manipulating variable) to the process and the output (process variable) from the process, and a phase difference between the input and the output are checked as the characteristics of the frequency. In this way, the frequency characteristics relating to the gain and phase of the process are measured.
In this method, the sine wave signal is input to the process for a long time, and the measurement is performed with the open loop. Therefore, it is difficult to apply it to the actual process.
In the correlation method, a white noise signal containing many frequency components is used for the identification signal to be superposed on the controlling signal to the process. The power spectrum ratio is obtained using a ratio of the auto-correlation function of the input and that of the output. The power spectrum ratio is used for obtaining the frequency characteristics of gain and phase of the process.
This method uses the identification signal containing many frequency components. Therefore, the method is superior to the servo analyzer method in that the measuring time is short. However, it is disadvantageous in that the amount of data to be processed is great, and that the frequency characteristics obtained are not exact.
The ARMA model method is a systematic method which can measure the dynamic characteristic of the process even under the closed loop control, if the identification conditions are satisfied. In this respect, this method has widely been used in recent days. If e.sup.j.omega..tau. is substituted into the time shift operator Z of the pulse transfer function, the pulse transfer function is transformed into the transfer function of the continuous system. The pulse transfer function is defined for the hold data for each sampling period. Therefore, in the vicinity of the Nyquist frequency, the gain and phase are apparently shifted due to the adverse effect of the sampling. Therefore, the pulse transfer function suffers from more errors than the transfer function in the continuous system. In designing the control system in the continuous system, the shift of gain and phase due to the sampling makes it difficult to design a limit for the control system since the shift occurs in high frequencies.